\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

↓

\[\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}

↓

\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)

double f(double x, double y, double z) {
        double r301084 = 1.0;
        double r301085 = 4.0;
        double r301086 = x;
        double r301087 = y;
        double r301088 = 0.25;
        double r301089 = r301087 * r301088;
        double r301090 = r301086 + r301089;
        double r301091 = z;
        double r301092 = r301090 - r301091;
        double r301093 = r301085 * r301092;
        double r301094 = r301093 / r301087;
        double r301095 = r301084 + r301094;
        return r301095;
}

↓

double f(double x, double y, double z) {
        double r301096 = 4.0;
        double r301097 = x;
        double r301098 = y;
        double r301099 = r301097 / r301098;
        double r301100 = 2.0;
        double r301101 = z;
        double r301102 = r301101 / r301098;
        double r301103 = r301096 * r301102;
        double r301104 = r301100 - r301103;
        double r301105 = fma(r301096, r301099, r301104);
        return r301105;
}

Derivation

Initial program 0.1
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
Taylor expanded around 0 0.0
\[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))

Error

Derivation

Reproduce